3.5.1 Outline the use of binary to represent data.
Computer systems are based on electrical circuitry. This means that electricity is either passing through the circuits or it isn't; it's either on or off, 1 or 0. Within a computer system each 1 and 0 is called a bit, and every 8 bits are referred to as a byte. Humans use this ability to their advantage by making machines perform calculations in base 2 instead of the traditional base 10. The table below provides an example of this:
Decimal number
128
64
32
16
8
4
2
1
Power of 2
2^7
2^6
2^5
2^4
2^3
2^2
2^1
2^0
Binary number
10000000
01000000
00100000
00010000
00001000
00000100
00000010
00000001
3.5.2 Outline the need for standard formats for storing documents and files..
Standard file formats are incredibly useful, simply because it means that the same file can be viewed in different computers, sometimes using different programs, and even Operating Systems. Examples of these include .jpg for images and .doc for word documents.
3.5.3 Express numbers in the bases: decimal, binary and hexadecimal.
The same number can be displayed using different bases, in this case base 2 (Binary), base 10 (Decimal) and base 16 (Hexadecimal). The table below shows how to count in each of these bases:
Name
Base
Digits
Binary
2
0, 1
Decimal
10
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Hexadecimal
16
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
3.5.4 Convert integers between the bases specified in 3.5.3 (maximum 8 bits)..
The table below shows the same numbers represented in different bases:
3.5.5 Apply binary notation to represent integers, both positive and negative, using the method-of-Two’s complement.
Working with negative numbers in binary notation is fairly simple, as all you need to do is use Two's co
mplement. There are two methods to do this. The first involves actually calculating the numbers using the usual 'Conversion Table' such as the one shown in 3.5.1, except that, in this case, the the decimal number 128 is swapped by -128. This means that now, instead of adding 128 units to the number by adding a 1 in this column you are subtracting 128 units, which now means that your entire number has now become negative, although this does not convert 50 into -50, it turns, for example, 1 into -127, or 10 into -118. to convert 1 into -1 you must use Two's complement. This consists of having, for example, the number 01010101 and inverting all of the numbers, except the last digit, as to end with the number 10101011. This is explained in the diagram below:
3.5.6 Define analogue data and digital data.
Analogue data refers to the transfer of energy in the form of, generally, an electromagnetic wave such as light. All EM waves are transverse and are of a sinusoidal shape. This means that they transfer energy with an amplitude that constantly varies. Digital data is generally consistent of only 1's and 0's.
3.5.7 Outline the need for the interconversion of data between analogue and digital formats for computer processing.
When telephones were first invented they used analogue data as a means to transfer energy. This meant that the world was filled with cables that transferred this type of data. With the arrival of computers this became an issue as computers work on digital data, not analogue, which meant that data to be converted from analogue to digital, using an ADC (Analogue to Digital Converter). This is the opposite of DAC (Digital to Analogue Converter). The actual process is outlined in the animated .gif to the right.
Curiously the Sony VAIO logo seen below has an interesting meaning behind it that you might not have been aware of before. the V and the A together stand for the analogue signal, and the I and O stand for the digital signal.
3.5.8 Discuss two applications that require conversion of data between analogue and digital formats including temperature sensing.
1. Most sensors work on a basis of recording analogue data such as temperature. This, however, means that the computer cannot interpret the data as computers only work on digital data, because of the nature of electrical signals. This means that an ADC is required to interpret the data.
2. DAC converters might be used, for example, for your computer's speakers, as the data required here is analogue. This means that the DAC converts the digital computer signals to analogue signals which are converted by the speakers into sound waves.
3.5.1 Outline the use of binary to represent data.
Computer systems are based on electrical circuitry. This means that electricity is either passing through the circuits or it isn't; it's either on or off, 1 or 0. Within a computer system each 1 and 0 is called a bit, and every 8 bits are referred to as a byte. Humans use this ability to their advantage by making machines perform calculations in base 2 instead of the traditional base 10. The table below provides an example of this:
3.5.2 Outline the need for standard formats for storing documents and files..
Standard file formats are incredibly useful, simply because it means that the same file can be viewed in different computers, sometimes using different programs, and even Operating Systems. Examples of these include .jpg for images and .doc for word documents.
3.5.3 Express numbers in the bases: decimal, binary and hexadecimal.
The same number can be displayed using different bases, in this case base 2 (Binary), base 10 (Decimal) and base 16 (Hexadecimal). The table below shows how to count in each of these bases:
3.5.4 Convert integers between the bases specified in 3.5.3 (maximum 8 bits)..
The table below shows the same numbers represented in different bases:
3.5.5 Apply binary notation to represent integers, both positive and negative, using the method-of-Two’s complement.
Working with negative numbers in binary notation is fairly simple, as all you need to do is use Two's co
mplement. There are two methods to do this. The first involves actually calculating the numbers using the usual 'Conversion Table' such as the one shown in 3.5.1, except that, in this case, the the decimal number 128 is swapped by -128. This means that now, instead of adding 128 units to the number by adding a 1 in this column you are subtracting 128 units, which now means that your entire number has now become negative, although this does not convert 50 into -50, it turns, for example, 1 into -127, or 10 into -118. to convert 1 into -1 you must use Two's complement. This consists of having, for example, the number 01010101 and inverting all of the numbers, except the last digit, as to end with the number 10101011. This is explained in the diagram below:
3.5.6 Define analogue data and digital data.
Analogue data refers to the transfer of energy in the form of, generally, an electromagnetic wave such as light. All EM waves are transverse and are of a sinusoidal shape. This means that they transfer energy with an amplitude that constantly varies. Digital data is generally consistent of only 1's and 0's.
3.5.7 Outline the need for the interconversion of data between analogue and digital formats for computer processing.
When telephones were first invented they used analogue data as a means to transfer energy. This meant that the world was filled with cables that transferred this type of data. With the arrival of computers this became an issue as computers work on digital data, not analogue, which meant that data to be converted from analogue to digital, using an ADC (Analogue to Digital Converter). This is the opposite of DAC (Digital to Analogue Converter). The actual process is outlined in the animated .gif to the right.
Curiously the Sony VAIO logo seen below has an interesting meaning behind it that you might not have been aware of before. the V and the A together stand for the analogue signal, and the I and O stand for the digital signal.
3.5.8 Discuss two applications that require conversion of data between analogue and digital formats including temperature sensing.
1. Most sensors work on a basis of recording analogue data such as temperature. This, however, means that the computer cannot interpret the data as computers only work on digital data, because of the nature of electrical signals. This means that an ADC is required to interpret the data.
2. DAC converters might be used, for example, for your computer's speakers, as the data required here is analogue. This means that the DAC converts the digital computer signals to analogue signals which are converted by the speakers into sound waves.
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